Recent content by cilla

Yeah. I know. You do the base step, then the induction step. I didn't have the starting form right, was confused about what I was supposed to actually be proving... I was just thinking to prove the k+1 part but what I'm supposed to be proving is that the initial recurrence relation formula given...

What's that formula for though? For proof by induction I need to make ##a_{k+1} = (k+1) + 2^{k+1} -1## right?

Yeah that's what I did. So how do I prove my solution by induction?

Homework Statement [/B] Solve the recurrence relation (use iteration). an = an-1 + 1 + 2n-1 a0 = 0 Then prove the solution by mathematical induction. Homework EquationsThe Attempt at a Solution a1 = 2 a2 = 5 a3 = 10 a4 = 19 a5 = 36 The solution appears to be an = n + 2n - 1 How are we...

I see your point thanks a lot.

Homework Statement [/B] Let X = {a,b}. A palindrome over X is a string α for which α = αR (i.e., a string that reads the same forward and backward). An example of a palindrome over X is bbaabb. Define a function from X* to the set of palindromes over X as f(α) = ααR. Is f one-to-one? Is f...

GFauxPas: The most I know of calculus is pre-, and that I took years ago (my most recent math class prior to this one). So as you might guess I'm very much out of practice. I found a counterexample for f being injective: f(1/2) = 2/5 = f(2). Thus the function is not one-to-one. As for f being...

How do you simplify a/(1+a^2) = (a+h)/(1+(a+h)^2) to a = a+h ?

Thanks RUber but I still don't know how to execute that...

Oh whoops, thanks Mark44. It is the latter. Can't change the post title unfortunately but I fixed it in the body.

Homework Statement Prove whether the function f(x) = x/(1+x^2) with domain & codomain = reals is one-to-one, onto, or both. Homework EquationsThe Attempt at a Solution I know to show if it's one-to-one I have to show a/(1+a^2) = b/(1+b^2), ultimately that a = b, I don't know how to simplify...

Oh yes, thank you gopher_p (and da_nang). I'm just glad it's not some crazy mix of inner and outer elements.

How are you supposed to go about putting together the power set of a set of sets such as X = {{1},{1,2}} What is the power set of X then? And what's the rule for calculating cardinality for the power set of a set that consists of elements which are sets such as the above? Because the set X...